The FEAST algorithm [5] is an algorithm aimed at solving generalized eigenvalue problems AX = BXΛ, where A,B are n×n matrices. In [4] we presented a short analysis of FEAST involving this eigenvalue problem. In the present work we focus on the real symmetric eigenvalue problem AX = XΛ, where A = A, XX = I and Λ is a diagonal matrix consisting of real eigenvalues. These eigenvalues are sought in...

A fast current pulse causes a material to heat and undergo rapid expansion. We calculate the response of a cylindrically shaped material to a pulse on the microsecond time scale. The first step is to obtain the breathing modes of elastic oscillation of the cylinder. These modes are calculated using a Rayleigh–Ritz variational method introduced by Demarest for cubes. The boundary conditions are ...

In this paper we present a study on the analogous properties of discrete and continuous Sturm-Liouville problems arising in matrix analysis and differential equations, respectively. Green’s functions in both cases have analogous expressions in terms of the spectral data. Most of the results associated to inverse problems in both cases are identical. In particular, in both cases Weyl’s m-functio...

20 LLE Review, Volume 73 In recent years, several authors1–14 have studied the linear growth of the Rayleigh–Taylor (RT) instability in ablation fronts accelerated by laser irradiations. The determination of the instability growth rate is crucial to the success of inertial confinement fusion (ICF)15,16 because an excessive distortion of the front could lead to a severe degradation of the capsul...

The topic of this paper is the convergence analysis of subspace gradient iterations for the simultaneous computation of a few of the smallest eigenvalues plus eigenvectors of a symmetric and positive definite matrix pair (A,M). The methods are based on subspace iterations for A−1M and use the Rayleigh-Ritz procedure for convergence acceleration. New sharp convergence estimates are proved by gen...

A new two-eigenfunctions theory, using the amplitude deflection and the generalized curvature as two fundamental eigenfunctions, is proposed for the free vibration solutions of a rectangular Mindlin plate. The three classical eigenvalue differential equations of a Mindlin plate are reformulated to arrive at two new eigenvalue differential equations for the proposed theory. The closed form eigen...

The method of intermediate problems of Weinstein and Aronszajn (cf. [19, 20]) provides a means of calculation for bounds to eigenvalues complementary to the Rayleigh{Ritz bounds. Convergence theorems for the method of intermediate problems in a generality that includes problems with essential spectra can be found in [5, 7{9, 12]. This paper supplements the general convergence theorems of [7, 9]...

An easy-to-implement method to measure relevant elastic and damping properties of the constituents of a sandwich structure, possibly with a heterogeneous core, is proposed. The method makes use of a one-point dynamical measurement on a thick plate. The hysteretic model for each (possibly orthotropic) constituent is written generically as “E(1 + jη)” for all mechanical parameters. The estimation...